Find the family of curves, the subtangent at any point of which is the arithmetic mean of the co-ordinate point of tangency.

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

The family of curves in which the subtangent at any point to any curve is double the abscissa is given by

The family of curves in which the sub-tangent at any point to any curve is double the abscissa is given by

The length of the subtangent at any point on the curve y=be^(x/3) is

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .